The Houston Rockets' Chris Paul (3) talks with teammate James Harden (13) as Clint Capela (15) shoots a free throw during the first quarter against the Miami Heat at the AmericanAirlines Arena in Miami on Wednesday, Feb. 7, 2018. (David Santiago/El Nuevo Herald/TNS)

The Houston Rockets' Chris Paul (3) talks with teammate James Harden (13) as Clint Capela (15) shoots a free throw during the first quarter against the Miami Heat at the AmericanAirlines Arena in Miami on

Houston Rockets guard James Harden, left, looks for an open teammate past Miami Heat guard Josh Richardson during the second half of an NBA basketball game, Wednesday, Feb. 7, 2018, in Miami. The Rockets

The Miami Heat's Tyler Johnson passes the ball away from the Houston Rockets' Gerald Green, right, during the first quarter at the AmericanAirlines Arena in Miami on Wednesday, Feb. 7, 2018. (David Santiago/El

The Houston Rockets' James Harden, right, blocks a shot by the Miami Heat's Derrick Jones Jr. during the first quarter at the AmericanAirlines Arena in Miami on Wednesday, Feb. 7, 2018. (David Santiago/El Nuevo Herald/TNS)

The Houston Rockets' James Harden, right, blocks a shot by the Miami Heat's Derrick Jones Jr. during the first quarter at the AmericanAirlines Arena in Miami on Wednesday, Feb. 7, 2018. (David Santiago/El Nuevo

The Miami Heat's Goran Dragic shoots over the Houston Rockets' Chris Paul, right, during the first quarter at the AmericanAirlines Arena in Miami on Wednesday, Feb. 7, 2018. (David Santiago/El Nuevo Herald/TNS)

The Miami Heat's Goran Dragic shoots over the Houston Rockets' Chris Paul, right, during the first quarter at the AmericanAirlines Arena in Miami on Wednesday, Feb. 7, 2018. (David Santiago/El Nuevo Herald/TNS)

Photo: David Santiago/TNS

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The Miami Heat's Josh Richardson goes to the basket between the Houston Rockets' Luc Mbah a Moute (12) and PJ Tucker (4) during the first quarter at the AmericanAirlines Arena in Miami on Wednesday, Feb. 7, 2018. (David Santiago/El Nuevo Herald/TNS)

The Miami Heat's Josh Richardson goes to the basket between the Houston Rockets' Luc Mbah a Moute (12) and PJ Tucker (4) during the first quarter at the AmericanAirlines Arena in Miami on Wednesday, Feb. 7,

The Houston Rockets' James Harden, right, blocks a shot by the Miami Heat's Derrick Jones Jr. during the first quarter at the AmericanAirlines Arena in Miami on Wednesday, Feb. 7, 2018. (David Santiago/El Nuevo Herald/TNS)

The Houston Rockets' James Harden, right, blocks a shot by the Miami Heat's Derrick Jones Jr. during the first quarter at the AmericanAirlines Arena in Miami on Wednesday, Feb. 7, 2018. (David Santiago/El Nuevo

The Miami Heat's Goran Dragic, left, drives against the Houston Rockets' Luc Mbah a Moute (12) during the first quarter at the AmericanAirlines Arena in Miami on Wednesday, Feb. 7, 2018. (David Santiago/El

The Miami Heat's Hassan Whiteside, right, shoots over the Houston Rockets' Clint Capela during the first quarter at the AmericanAirlines Arena in Miami on Wednesday, Feb. 7, 2018. (David Santiago/El Nuevo

Alonzo Mourning, left, Miami Heat vice president of player programs, presents guard Goran Dragic his NBA All-Star Game jersey during a ceremony before the start of an NBA basketball game against the Houston

Houston Rockets head coach Mike D'Antoni calls out a play during the second half of an NBA basketball game against the Miami Heat, Wednesday, Feb. 7, 2018, in Miami. The Rockets defeated the Heat 109-101. (AP Photo/Wilfredo Lee)

Houston Rockets head coach Mike D'Antoni calls out a play during the second half of an NBA basketball game against the Miami Heat, Wednesday, Feb. 7, 2018, in Miami. The Rockets defeated the Heat 109-101. (AP

Houston Rockets guard Gerald Green, right, grabs a rebound as Miami Heat forward James Johnson attempts to block a shot during the second half of an NBA basketball game, Wednesday, Feb. 7, 2018, in Miami. The

Houston Rockets forward Luc Mbah a Moute (12) goes up for a shot against Miami Heat forward James Johnson (16) during the second half of an NBA basketball game, Wednesday, Feb. 7, 2018, in Miami. The Rockets

Miami Heat guard Goran Dragic (7) reacts after a play during the second half of an NBA basketball game against the Houston Rockets, Wednesday, Feb. 7, 2018, in Miami. The Rockets defeated the Heat 109-101. (AP Photo/Wilfredo Lee)

Miami Heat guard Goran Dragic (7) reacts after a play during the second half of an NBA basketball game against the Houston Rockets, Wednesday, Feb. 7, 2018, in Miami. The Rockets defeated the Heat 109-101. (AP

Miami Heat center Hassan Whiteside (21) lands on top of Houston Rockets forward Luc Mbah a Moute (12) after Whiteside attempted to block a shot during the second half of an NBA basketball game, Wednesday, Feb.

Houston Rockets guard James Harden celebrates a three-point shot during the second half of an NBA basketball game against the Miami Heat, Wednesday, Feb. 7, 2018, in Miami. The Rockets defeated the Heat 109-101. (AP Photo/Wilfredo Lee)

Houston Rockets guard James Harden celebrates a three-point shot during the second half of an NBA basketball game against the Miami Heat, Wednesday, Feb. 7, 2018, in Miami. The Rockets defeated the Heat

MIAMI – The Rockets were running on fumes, but they were good fumes. They might not have had much left in the final hours of the road trip, but what they had made a statement that could be as telling as any along the way.

The Rockets' 109-101 win against the Miami Heat might be forgotten in the waves of games, but the determination to persevere could be as telling as anything they had done in a win in San Antonio or the romp in Cleveland to start the trip.

Shorthanded with three regulars out, and shorter on rest, with a 3:45 a.m. arrival at the Miami hotel for the second half of a back-to-back, the Rockets blew past the Heat with a finishing kick as James Harden drained consecutive 3-pointers to put away the win, finishing with 41 points, six assists and three steals. Chris Paul had 24 points, seven rebounds and seven assists. And the Rockets made 51.4 percent of their shots, moving to 28-2 the past two seasons when making half their attempts.

With a six-game winning streak, the Rockets are 40-13, the best record in franchise history through 53 games. The latest win came with Eric Gordon, Trevor Ariza and Ryan Anderson out, and withstood the drive of the Heat backcourt.

For much of the game, the Rockets' fatigue was clear, and helped the Heat keep it tight.

Big men switching did not have the quickness on the perimeter. Perimeter players put on Heat centers gave up ground inside. Rebounds fell uncontrolled.

Most of all, the Rockets spent much of the game after their initial burst struggling to get energy in their offense. Through three quarters, they had just five fast-break points. But even in the halfcourt, they moved the ball slowly, often forcing them to take contested shots to beat the shot clock.

The league's top defensive rebounding team all season, the Rockets were beaten badly on the boards, with the Heat getting 11 offensive rebounds through three quarters and two more to start the fourth, putting them within three of the most the Rockets had surrendered in a game this season with 10 minutes still to play.

When the Heat took advantage of the extra shots to regain the lead, Harden returned with nine minutes left and the Rockets answered with a much-needed burst of scoring. Harden drove the baseline to a slam then hit a 3-pointer. Paul put in a mid-range jumper. And with a Clint Capela tip, the Rockets led by seven.

They still seemed to be barely hanging on, with Josh Richardson, who had a career high 30 points, and Goran Dragic able to trade punches with Harden and Paul.

Finally, the Rockets opened a cushion when Harden dropped in another 3 with 2:51 left and Capela began controlling the boards as the Rockets could not all season. When Harden put in another, the Rockets had one of their toughest wins of the season and a statement different from the loud and clear wins on the way to Miami.

The Rockets had seemed in control early, with Harden dominating off the dribble by repeatedly toasting switches with an array of unfair one-on-one moves. When he hit a step-back 3 midway through the second quarter, the Rockets held a 17-point lead.

Dragic answered, but Harden went to the rim as he had through much of the half, giving him 23 points with 5:10 left in the half and the Rockets a 55-39 lead.

The Rockets, however, seemed to have punched themselves out. They had begun the game with good energy, as if determined to push through the back-to-back fatigue. But late in the half, they were slow to get into their offense, taking contested shots and unable to slow Dragic on the other end.

The Heat rolled through an 18-6 run to close the half, repeatedly burning the Rockets' switches with either Hassan Whiteside in the post or Dragic off the dribble. Dragic scored 10 of his 20 first-half points in the final 2:03 of the half, trimming the Rockets' 17-point lead to just four.

For all they had done to build the lead, the Rockets had fallen into a halfcourt game, getting little from their frontcourt offensively and showing few signs that they could get the stops that had built the lead.

They got enough for one last kick to put the game away and to prove something along the way.